Good question. If I remember correctly, Berkeley teaches from it and one person I respect agreed it was good. I think the impenetrability was consider more of a feature than a bug by the person doing the recommending. IOW, he was assuming that people taking my recommendations would be geniuses by-and-large and that the harder book would be better in the long-run for the brightest people who studied from it.
Part of my motivation for posting this here was to improve my recommendations. So I’m happy to change the rec to something more accessible if we can crowd-source something like a consensus best choice here on LW that’s still good for the smartest readers.
[he was assuming that] people taking my recommendations would be geniuses by-and-large and that the harder book would be better in the long-run for the brightest people who studied from it.
Is this actually true? My current guess is that even though for a given level of training, smarter people can get through harder texts, they will learn more if they go through easier texts first.
Is this actually true? My current guess is that even though for a given level of training, smarter people can get through harder texts, they will learn more if they go through easier texts first.
I think you’re right here (enough so that you beat me to my reply nearly verbatim.)
Furthermore, a hard to use text may be significantly less hard to use in the classroom where you have peers, teachers, and other forms of guidance to help digest the material. Recommendations for specialists working at home or outside a classroom might not be the same as the recommendations you would give to someone taking a particular class at Berkeley or some other environment where those resources are available.
A flat out bad textbook might seem really good when it is something else such as the teacher, the method, or the support that makes the book work.
I haven’t read multiple discrete math textbooks, so I can’t make a comparative judgment, but I can confirm that Concrete Mathematics is a delightful and useful text.
Also, while Sipser’s book is great for theoretical computer science, I think Moore’s The Nature of Computation is much better, at least in terms of being fun to read.
My recollection of Berkeley’s discrete math course (compsci-oriented version that also emphasizes probability heavily) was that it was taught mostly from some pretty nice lecture notes. Looks like the lecture notes from the Fall 2012 compsci version of the course are available for download from the course website.
It occurred to me the other year that lecture notes could be a good way to learn things in general, or at least pick up the basics of a subject:
There’s no incentive for instructors to pad them to appease publishers.
Unlike textbooks or Wikipedia, they’re being updated constantly based on what seems to work for explaining concepts most effectively.
They’re often available freely for download. (site:youruniversity.edu yoursubject on Google, OCWs, etc.)
They’re probably written to communicate understanding rather than achieve perfect rigor.
If you know how long the corresponding lecture took, you can set a timer for that length of time (or 0.8 times as long, or whatever) and aim to get through the lecture notes before the timer rings (taking notes if you want; keep glancing at the timer and your progress to calibrate your speed). This is a pretty good motivational hack, in my experience. I like it better than attending an actual lecture because I can dive deeper or skim over stuff as I like, so it’s kind of like a personalized version of the lecture. I don’t worry if I end up skimming over some stuff and not understanding it perfectly—I don’t understand everything in a “real” lecture either (much less, really).
They break the course material in to nice manageable chunks: if the class covered one set of notes per day, for instance, you could do the same in your self-study. (Don’t Break the Chain and BeeMinder come to mind as macro-level motivational hacks that may be useful.)
I think the impenetrability was consider more of a feature than a bug by the person doing the recommending. IOW, he was assuming that people taking my recommendations would be geniuses by-and-large and that the harder book would be better in the long-run for the brightest people who studied from it.
You must have misremembered; Rosen’s text is very verbose and clear. It will certainly be an elementary text for any second-year or higher math undergraduate.
The book is partly designed to be a crash course in math for CS students, so there are introductory chapters on proofs, logic, sets, etc., with plenty of examples. Exercises are mainly drills and computations, with a smaller proportion of exercises on proofs.
As for the bad Amazon reviews—many students using this textbook will be encountering mathematical proofs for the first time, so frustration from some of the students is to be expected. I don’t think the reviews are representative of the book.
All in all, the text serves its purpose well as an introductory math book for CS undergraduates. I think its greatest downfall is its excessive verbosity—there is so much redundancy that examples take up around half the book.
Good question. If I remember correctly, Berkeley teaches from it and one person I respect agreed it was good. I think the impenetrability was consider more of a feature than a bug by the person doing the recommending. IOW, he was assuming that people taking my recommendations would be geniuses by-and-large and that the harder book would be better in the long-run for the brightest people who studied from it.
Part of my motivation for posting this here was to improve my recommendations. So I’m happy to change the rec to something more accessible if we can crowd-source something like a consensus best choice here on LW that’s still good for the smartest readers.
Is this actually true? My current guess is that even though for a given level of training, smarter people can get through harder texts, they will learn more if they go through easier texts first.
I think you’re right here (enough so that you beat me to my reply nearly verbatim.)
Furthermore, a hard to use text may be significantly less hard to use in the classroom where you have peers, teachers, and other forms of guidance to help digest the material. Recommendations for specialists working at home or outside a classroom might not be the same as the recommendations you would give to someone taking a particular class at Berkeley or some other environment where those resources are available.
A flat out bad textbook might seem really good when it is something else such as the teacher, the method, or the support that makes the book work.
I haven’t read multiple discrete math textbooks, so I can’t make a comparative judgment, but I can confirm that Concrete Mathematics is a delightful and useful text.
Also, while Sipser’s book is great for theoretical computer science, I think Moore’s The Nature of Computation is much better, at least in terms of being fun to read.
My recollection of Berkeley’s discrete math course (compsci-oriented version that also emphasizes probability heavily) was that it was taught mostly from some pretty nice lecture notes. Looks like the lecture notes from the Fall 2012 compsci version of the course are available for download from the course website.
It occurred to me the other year that lecture notes could be a good way to learn things in general, or at least pick up the basics of a subject:
There’s no incentive for instructors to pad them to appease publishers.
Unlike textbooks or Wikipedia, they’re being updated constantly based on what seems to work for explaining concepts most effectively.
They’re often available freely for download. (site:youruniversity.edu yoursubject on Google, OCWs, etc.)
They’re probably written to communicate understanding rather than achieve perfect rigor.
If you know how long the corresponding lecture took, you can set a timer for that length of time (or 0.8 times as long, or whatever) and aim to get through the lecture notes before the timer rings (taking notes if you want; keep glancing at the timer and your progress to calibrate your speed). This is a pretty good motivational hack, in my experience. I like it better than attending an actual lecture because I can dive deeper or skim over stuff as I like, so it’s kind of like a personalized version of the lecture. I don’t worry if I end up skimming over some stuff and not understanding it perfectly—I don’t understand everything in a “real” lecture either (much less, really).
They break the course material in to nice manageable chunks: if the class covered one set of notes per day, for instance, you could do the same in your self-study. (Don’t Break the Chain and BeeMinder come to mind as macro-level motivational hacks that may be useful.)
You must have misremembered; Rosen’s text is very verbose and clear. It will certainly be an elementary text for any second-year or higher math undergraduate.
The book is partly designed to be a crash course in math for CS students, so there are introductory chapters on proofs, logic, sets, etc., with plenty of examples. Exercises are mainly drills and computations, with a smaller proportion of exercises on proofs.
As for the bad Amazon reviews—many students using this textbook will be encountering mathematical proofs for the first time, so frustration from some of the students is to be expected. I don’t think the reviews are representative of the book.
All in all, the text serves its purpose well as an introductory math book for CS undergraduates. I think its greatest downfall is its excessive verbosity—there is so much redundancy that examples take up around half the book.